Packings of monodisperse emulsions in flat microfluidic channels

In the lateral confinement of a flat microfluidic channel, monodisperse emulsion droplets spontaneously self-organize in a variety of topologically different packings. The explicit construction of mechanically equilibrated arrangements of effectively two-dimensional congruent droplet shapes reveals the existence of multiple mechanical equilibria depending on channel width W, droplet area Ad, and volume fraction φ of the dispersed phase. The corresponding boundaries of local or global stability are summarized in a packing diagram for congruent droplet shapes in terms of the dimensionless channel width w=W/√Ad and φ. In agreement with experimental results, an increasingly strong hysteresis of the transition between single-row and two-row packings is observed during changes of w above a threshold volume fraction of φ∗≃0.813.